In recent years, devices which deal with color images, such as scanners, digital cameras, monitors, printers, projectors and so forth, have spread rapidly. When color images are to be handled between these devices, the colors change in appearance in accordance with characteristics of the devices. Consequently, color reproduction between devices has become problematic, and proposals for accurate color reproduction methods are desired.
In order to match colors between devices, it is necessary to ascertain beforehand color characteristics that the devices have. With outputting and measuring all colors (for example, with 24-bit color, 16,777,216 colors) in order to ascertain color characteristics of a device, the number of colors is very large and this is not practical. Therefore, color sampling is performed, and estimation of all colors from measured values is performed.
To estimate all colors, it is common to employ linear interpolation which, as shown in FIG. 16A, interpolates from measured sampling points and finds an interpolation point, curvilinear interpolation which, as shown in FIG. 16B, estimates curves (1) to (3) from measured sampling points, estimates a curve (4) from points on the curves and finds an interpolation point, or the like. Because color characteristics of a device cannot be expressed with linear forms, results which are obtained by linear interpolation have poor accuracy, so interpolation is performed using curvilinear interpolation.
However, as another color reproduction method, a technology described in, for example, Japanese Patent Application Laid-Open (J-PA) No. 2001-283210 has been proposed. In the technology described in JP-A No. 2001-283210, coefficients of a matrix calculation equation of relationship equations are varyingly controlled such that differences between tristimulus values of colors which are calculated using the relationship equations, from three primary color values for outputting the colors, and tristimulus values of the colors which are obtained by spectroscopic analysis are minimized. From reference tristimulus values of the colors, which have been prepared in advance, and values of the three primary colors, which output the colors to appear as colors the same as these colors, learning is implemented with a neural network back propagation method or the like, and residuals are calculated on the basis of non-linear forms. A linear variation matrix and residuals are determined, and a profile is created. Hence, it is proposed that colors of images which are outputted from image output means will match colors obtained by spectroscopic analysis.